Full text of DOI:10.1557/mrs2001.43

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cally slightly smaller than 3 and depends
also on temperature. Thus, already the in-
dividual polymer chain with its almost
O(3N) degrees of freedom needs a statis-
tical mechanical description. Depending
on solvent properties, the chain in solu-
tion can be expanded (ꢀR2ꢁ ꢂ Nꢃ, ꢃ ꢂ 3/5,
where ꢀR2ꢁ is the mean-squared extension
of the chain), if in a good solvent. In mar-
ginal or ꢄ-solvent, where the monomer–
monomer attraction just compensates the
mutual chain–chain excluded volume,
one finds that ꢃ ꢀ 1/2, while chains in
poor solvent collapse into a dense globule
and precipitate out of solution. In a melt,
the other chains essentially act as a mar-
ginal solvent, resulting in ꢃ ꢀ 1/2. Some
polymers crystallize, displaying very rich
kinetics. Mixtures of polymers pose spe-
cial problems, as tiny differences in the
interaction energy are sufficient to initiate
phase separation, since the interaction is
to be compared with the translational and
not the conformational entropy of the
overall chain. A striking example is the
phase-separation of hydrogenated and
deuterated polystyrene (PS) for long
enough chains.
Multiscale Problems
in Polymer
Science: Simulation
Approaches
K. Kremer and F. Müller-Plathe
Polymer materials range from indus-
trial commodities, such as plastic bags, to
high-tech polymers used for optical appli-
cations, and all the way to biological sys-
tems, where the most prominent example
is DNA. They can be crystalline, amorphous
(glasses, melts, gels, rubber), or in solution.
Polymers in the glassy state are standard
materials for many applications (yogurt
cups, compact discs, housings for techni-
cal equipment, etc.). They often combine
relatively low specific weight with ductil-
ity, and they can be processed at moderate
temperatures. In the melt state, polymers
are viscoelastic liquids. Added to a sol-
vent, polymers can be used as either shear-
thickening or shear-thinning viscosity
modifiers. Polymer networks form gels or
rubber. Applications range from gels in
(e.g., low-fat) foods, to hydrogels used in
modern body care (e.g., diapers), to bio-
logical systems (cytoskeletons), and all the
way to classical elastomers (e.g., car tires).
This range of applications is due to the
variability of physical properties, which is
based on the many different molecular
building blocks, molecular architectures,
and molecular weights of polymers. It is the
combination and the rather subtle inter-
play of local chemical and more global ar-
chitectural and size properties that makes
macromolecules so versatile. This means
that many different length and time scales
are relevant; understanding the properties
on one scale is not sufficient.
bisphenol-A polycarbonate (BPA-PC) (e.g.,
compact discs). There are also many
complex cases (e.g., DNA, proteins, co-
polymers), where several different build-
ing blocks are present in one molecule.
While most polymers are not water-soluble,
poly(ethylene oxide) (PEO) has the excep-
tional property of being both water- and
oil-soluble. Other water-soluble polymers
include polyelectrolytes, which dissociate
ions into water and stay in solution even
if their backbone is hydrophobic. Al-
though polyelectrolytes are beyond the
scope of this article, the typical simulation
approaches for polyelectrolytes are con-
ceptually very similar to the ones dis-
cussed here.1–4
Current research deals with more com-
plicated architectures, such as star poly-
mers, dendritic structures, cross-linked
systems, and so on. Another special class
are block copolymers. These range from
long chains consisting of blocks of A and B
repeat units to random copolymers or ob-
jects containing flexible and rigid pieces.
Though of utmost scientific and technical
interest, they will not be discussed here.5
Length andTime Scales
for Polymer Simulations
Architecture/Morphology:
Universal Structural Aspects
Let us start with the shear viscosity ꢅ of
a polymer melt, which illustrates the whole
complexity of the problem. If one changes
the process temperature of a BPA-PC melt
from 500 K to 470 K, the viscosity rises by
a factor of 10. This effect is a direct result
of interactions on the atomistic level, as
it could also have been achieved by an
equivalent change in the chemical struc-
ture of the monomer. On the other hand,
increasing the chain length by a factor of
2 also shifts the viscosity by a factor of 10
because, for long chain melts, ꢅ ꢂ N3.4.
This power law is a universal polymer
The simplest polymers are long linear
objects of identical repeat units. Due to
their intrinsic flexibility, they can assume
distinct spatial conformations of the order
of O(qN), where q represents the number
of torsional states of the subsequent bonds,
and N is the number of repeat units in a
melt or solution. PE, for example, has stiff
bond angles between subsequent carbon–
carbon bonds. Each added bond is in
principle allowed to take one of the three
torsional states (trans, gaucheꢀ, or gaucheꢁ).
Due to excluded volume effects, q is typi-
Chemical Repeat Units:
Table I: Examples of Simple Polymers.
Material-Specific Aspects
The simplest polymers are chain mole-
cules with identical segments, repeat units,
or monomers. Examples are listed in Table I.
These simple examples range from
polyethylene (PE) (e.g., plastic bags) to
Polyethyelene (PE)
(CH2)n
Polystyrene (PS)
(CH2(CH(C6H5)))n
((CH2)2O)n
Poly(ethylene oxide) (PEO)
Bisphenol-A polycarbonate (BPA-PC)
((C6H4)C(CH3)2(C6H4)CO3)n
MRS BULLETIN/MARCH 2001
205

Multiscale Problems in Polymer Science: Simulation Approaches
property and holds for all known linear
polymers, independent of the chemical
structure of their backbone. Thus, both
material-specific as well as universal prop-
erties produce a comparable variation of
the dynamic macroscopic properties and
therefore of relevant time scales. This varia-
tion can easily extend over several orders
of magnitude.
At first sight, it might be tempting to
perform an all-atom computer simulation
of a polymer melt. However, there are sev-
eral complications. The first stems from
the choice of interaction potentials, while
the second is related to the many scales
involved. Such an all-atom simulation
uses a classical force field based on a clas-
sical energy function between all atoms.
All quantum simulations (Car–Parinello
density functional simulations, path inte-
gral quantum Monte Carlo simulations, or
combinations thereof) are still confined to
very small systems.1
Although the force-field approach sounds
conceptually straightforward, it contains a
number of unsolved complications. First,
although usually not considered, are quan-
tum effects. One might think that typical
temperatures for macromolecular systems
(room temperature and higher) are well
above the Debye temperature of the rele-
vant atoms. This is true for the carbon
atoms, but not necessarily for the many
hydrogen atoms present. Their thermal
de Broglie wavelength at room tempera-
ture is about 1 Å. A recent paper by
Martonak et al.6 revealed that even at
room temperature, quantum effects are
crucial to understanding the anisotropic
thermal expansion of PE crystals. Though
a rather special finding, it should be
kept in mind. For the classical force-field
approach, the intramolecular interaction
along the backbone is derived from a
parameterization of quantum calculations
of chain fragments. To parameterize
the nonbonded interactions, experimental
quantities are usually used, such as the
heat of vaporization of low-molecular-
weight liquids. It is often impossible to
optimize all properties to the same degree
of accuracy and confidence. Thus, one has
to be very careful, and there is no univer-
sal force field for a system that, without
further verification, can be used at sig-
nificantly different temperatures or for
different mixtures. Keeping this in mind,
force-field simulations can be very useful
and have provided many important in-
sights into microscopic properties over the
last few years.2,4
It is actually questionable whether such
a fully atomistic simulation, if possible,
would be useful at all. Almost all the in-
formation generated would be irrelevant
for the questions under consideration (e.g.,
the previously mentioned viscosity ꢅ). In
order to make suggestions for material
improvements, or to qualitatively and
quantitatively understand properties, it is
crucial to structure and understand the re-
sults rather than just collect measured
quantities. This is often easier with simpli-
fied models.
Polymers are characterized by a hier-
archy of different length and time scales.
Figure 1 illustrates this and shows the typi-
cal range involved. On the microscopic
level, the properties are dominated by the
local vibrations of bond angles. The typi-
cal time constant is about 10ꢁ13 s, resulting
in a simulation time step of about 10ꢁ15 s.
This angstrom regime is well character-
ized by the bond angles and bond lengths.
The properties on this level are solely de-
termined by all the details of the atoms or
molecules involved.
more or less flexible thread. This is the
universal entropy-dominated coil regime.
The many possible conformations of the
chains and the many ways to pack chains
in a melt determine the morphology. On
the mesoscopic level, many properties can
be understood on the basis of simple
coarse-grained (“bead spring”) models,
which represent chains as spherical beads
connected by anharmonic springs. Char-
acteristic time and length scales are indi-
cated in the figure. On the even coarser,
semimacroscopic level, the behavior is
dominated by the overall relaxation of the
chain conformations. Typical times depend
on chain length and vary between N2 and
N3.4. As explained before, prefactors origi-
nating from the microscopic interaction of
the monomers cause an equally large varia-
tion of scales. The resulting characteristic
times can reach seconds or more if one ap-
proaches the glass-transition temperature.
Thus, a satisfactory numerical description
of material properties needs a combination
of microscopic and coarse-grained models.
Mapping from Atomistic to
Mesoscopic Models—and Back
The successful mapping from an atom-
istic model to a mesoscale model has the
advantage that time and length scales are
accessible that are far beyond atomistic
simulations. Thus, qualitatively different
physical problems can be treated. A useful
mesoscale model preserves enough of the
original chemical identity of the atomistic
model to reproduce certain aspects of, say,
PS or polypropylene chains under the cor-
responding conditions. It is no surprise
that in recent years, a number of atomistic-
to-mesoscopic mappings have been pub-
lished (see, e.g., References 7–14; a review
encompassing scales bridging from elec-
tronic to macroscopic degrees of freedom
is presented in Reference 2).
On a more coarse-grained level, one
cannot resolve all atomistic details of the
chains anymore. The chain looks like a
Figure 1. Polymers exhibit phenomena on many length scales (from entire devices down to electrons) and associated time scales (from years to
femtoseconds). For details, see text.
206
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Multiscale Problems in Polymer Science: Simulation Approaches
It turns out that coarse-grained models
are useful not only for studying large-scale
phenomena; they are also a powerful tool
for the generation of well-equilibrated
atomistic structures, provided that one
can perform a reverse mapping from the
mesoscopic model back to a fully atom-
istic model. This is often needed because
experimental information involves atoms,
as in nuclear magnetic resonance spec-
troscopy,15 neutron scattering,8 or positron
annihilation spectroscopy.16
The approaches to coarse-graining vary
substantially; to date, no “standard” proce-
dure has emerged. The mesoscopic models
include both continuous models6,8–10 and
lattice models.11 – 14 For a given complexity
of the model (e.g., the range of the non-
bonded interactions), continuous and lat-
tice models seem to be roughly comparable,
as far as static polymer properties are
concerned. The continuous models have
advantages when it comes to dynamic
problems such as shear behavior or to
questions requiring changes in the simula-
tion volume (swelling properties, etc.). To
study dynamical quantities, continuous
models allow equations of motion (often
molecular or Brownian dynamics), which
are well-controlled approximations. Monte
Carlo calculations show physical dynamics,
but only if well-known standard criteria
for the motion of the beads are obeyed.1,3,17
Then the dynamics can be viewed as
Brownian. The most important condition
is that the motion is local, involving only a
small number of beads at a time.
dene group (S1), the other at the carbonate
moiety (S2). A reduction of the number of
interaction sites per monomer from 33 to 2
is thereby achieved. What remains of the
chemical identity of the polymer is con-
tained in four intrachain interactions: one
bond stretch (S1–S2), two bond angles
(S1–S2–S1 and S2–S1–S2) and one torsion
(S1–S2–S1–S2). These interactions are pa-
rameterized in three steps: First, the atom-
istic potential-energy surface of a fragment
is calculated by ab initio quantum chem-
istry. Second, with this potential surface,
a Monte Carlo calculation of a single
random-walk chain in free space is per-
formed, from which distributions of the
four intrachain degrees of freedom are
extracted. These distributions contain the
complete intrachain information of the
coarse-grained model chain. This infor-
mation is used in the third step, as the
distributions are transformed into an ef-
fective coarse-grained potential-energy
function (potential of mean force) by
simply taking the logarithm of the distri-
bution functions. This determines the
interaction potentials without any ad-
justable parameter or fitting. Taking the
melt density from experiments, with this
approach one is able to reproduce the shift
of the Vogel–Fulcher temperature T0 for
three different polycarbonate modifica-
tions almost quantitatively and the shift in
the generalized activation energy qualita-
tively, with energies in the right order of
magnitude. Taking this, one can estimate
viscosities; Figure 3 shows this for BPA-PC.
The interchain interactions are modeled
as purely repulsive in order to keep the
interactions short-ranged and the simula-
tions fast. The melt, however, has no in-
trinsic cohesion, but is kept together by
the constant-volume condition or an ap-
plied (high) pressure. This is acceptable, as
long as one is interested in bulk polymers
of known homogeneous density. When
the simulated system is expected to de-
velop density heterogeneities (e.g., in the
presence of several phases), or if one is
concerned about properties of free sur-
faces, one has to adapt the model. Work is
currently under way to develop attractive
coarse-grained potentials.11
Automatic Coarse-Graining
The systematic development of meso-
scopic polymer models based on first
principles is a cumbersome process. A
number of steps have to be made:
1. The degree of coarse-graining and the
positions of the coarse-grained beads in
relation to the atoms have to be determined.
2. The form of the intra- and interchain
potentials need to be chosen, as they can-
A successful example of mapping atom-
istic to coarse-grained models is the study
of different polycarbonate melts.7 In the
case of BPA-PC, the atomistic monomer is
mapped onto two coarse-grained beads
(Figure 2), one centered at the isopropyli-
Figure 2. Atomistic bisphenol-A
polycarbonate (BPA-PC) is mapped
onto a coarse-grained model consisting
of two beads per monomer, which are
centered at the isopropylidene and the
carbonate groups (from Reference 7).
Figure 3. Plot of the viscosity for BPA-PC determined from simulation of the coarse-grained
model and data taken from experiment. The simulation and experimental data are used to
extrapolate into the other regime within the Vogel–Fulcher (VF) scheme. The highest
temperature for experiment and the lowest for simulation is T ꢀ 500 K, allowing an
absolute time scaling (from Reference 7).
MRS BULLETIN/MARCH 2001
207

Multiscale Problems in Polymer Science: Simulation Approaches
not always be directly derived from the
distributions.
3. Free parameters, especially for the non-
bonded interactions, have to be optimized.
While (1) and (2) are intellectual chal-
lenges, (3) is often a menial task.
the effective interaction potentials cannot
be separated anymore, a direct Boltzmann
inversion to get the potential of mean
force would not properly count the inter-
actions in solution.
the reverse mapping is relatively straight-
forward. The atomistic monomers are
placed at or near the corresponding posi-
tions in space and oriented such that as
many as possible of their intrachain de-
grees of freedom are in low-energy con-
formations. Local stresses, close contacts
between different chains, and so on are
left to relax out by standard atomistic MD
simulations.21
In order to avoid these problems, the
same 23-mer of PAA was simulated with
the coarse-grained model. The coarse-
grained parameters were adjusted until
the target RDFs and other distributions
were reproduced satisfactorily. We defined
a least-squares merit function f (p1,p2,...)
which was minimized, where p1,p2,... are
the parameters in the optimization set. For
the minimization, we use a standard sim-
plex scheme.19 Note that every evaluation
of f involves an entire molecular-dynamics
(or Brownian-dynamics) simulation of the
coarse-grained system. Here, the appar-
ently straightforward scheme can become
technically tricky and computationally
expensive.
With the coarse-grained model parame-
terized, the simulation was extended to
much longer chains of PAA in aqueous
solution. The results for the calculated hy-
drodynamic radius of such chains closely
match the results from dynamic light scat-
tering (Figure 5). This shows that the
coarse-grained model retains enough of
the true identity of PAA to reproduce its
structure on a scale much larger than that
of the atomistic model from which it was
developed. In the meantime, this approach
has been extended not only to other poly-
mers in solution but also to bulk polymer
melts.20
This section describes a recent approach
to systematically and automatically parame-
terizing the interaction parameters of meso-
scale models. The purpose is to carry out
the parameterization (3) for a given choice
of degree of coarse-graining (1) and form
the potential (2) quickly and reproducibly.
We started by obtaining reference data.
These were structural properties of the
polymer of interest, the sodium salt of
poly(acrylic acid) (PAA) as an aqueous
solution of about 2 wt%. The data were
obtained by performing an atomistic simu-
lation of an oligomer (23 monomers) sol-
vated by about 3200 water molecules. The
coarse-grained model contained 1 bead
per monomer, centered at the center of
mass of the atomistic monomer, reducing
the number of polymer atoms by eight.
More importantly, the coarse-grained model
disposed of the explicit solvent, so that the
total number of sites was reduced from
approximately 3350 to 23 (Figure 4). The
coarse-grained intrachain interactions
consisted of a harmonic bond potential,
the multiple-minima bond-angle poten-
tial, and a short cosine expansion of the
dihedral-angle potential. The nonbonded
potential between monomers is pieced to-
gether from different factors. Such a po-
tential has proven useful,11 as it contains
enough flexibility to encompass an effec-
tive description of the solvent. The refer-
ence data include distributions of bond
lengths and bond angles as well as radial
distribution functions RDFtarget(r) obtained
from the atomistic simulation but calcu-
lated for the coarse-grained beads. Since
here the bonded and nonbonded parts of
Large equilibrated samples of BPA-PC
have been used to compare structure fac-
tors to neutron-scattering data.8 Simulation
and experiment compare very well (Fig-
ure 6), which indicates that the atomistic
structures generated by means of a coarse-
grained equilibration are faithful repre-
sentations of the microscopic structure of
BPA-PC. This was further supported by
an analysis of the polycarbonate structures
with a new method for the calculation of
positron lifetimes.16 Such large equilibrated
computer samples are now used for other
“applications,” where the atomistic details
are essential. One example of immediate
industrial relevance is the study of the
diffusion of the polycondensation by-
product phenol in BPA-PC melts.22 These
studies have not only led to a hitherto-
unknown mechanism of penetrant diffusion
in polymers, but also to more accurate
values of diffusion coefficients that have
already found their way into polycarbon-
ate production. None of these studies would
have been possible without the help of
systematic coarse-graining and the sub-
sequent fine-graining of polymer models.
Atomistic Results after
Reverse Mapping
After equilibration of coarse-grained
models, they can be mapped back to an
atomistic model. If the position of a
coarse-grained site is defined in terms of
the atom positions of the atomistic model,
Beyond Particle-Based
Chain Models
So far, the coarsening in terms of the
length scale was on a level such that a
given coarse-grained bead represented
Figure 5. The hydrodynamic radius
of PAA in aqueous solution as a
function of molecular weight (MW).
Experimental data courtesy of
Beate Müller and Simone Wiegand,
Max-Planck-Institut für
Figure 4. An example of mapping between atomistic and mesoscopic models: the sodium
salt of poly(acrylic acid) (PAA) (2 wt%) in aqueous solution (from Reference 18).
Polymerforschung (unpublished).
208
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Multiscale Problems in Polymer Science: Simulation Approaches
one DEC-Alpha processor, polymeric
melts of the order of several thousands of
ellipsoids to represent chains. Typical runs
consist of 10,000 ellipsoids. The procedure
is a standard Metropolis Monte Carlo
simulation for translation, rotation, and
shape-change of the ellipsoids. By doing
this, one is able to investigate phase sepa-
ration and morphology development of
micrometer-sized polymer samples. Hydro-
dynamic properties on a coarse-grained
level beyond the bead-spring chain pic-
ture without topological constraints can
be studied by dissipative particle dynam-
ics.28,29 There, the chains also can move
freely through each other. So far, this has
not been used for chain models, where the
properties of the “bead” are derived from
micro- or mesoscopic information.
Beyond such particle-based methods,
continuum approaches are used to study
the properties of macroscopic samples,
such as the finite element method.30 Re-
cently, this approach was combined with
Monte Carlo techniques in order to study
composite materials by Gusev et al.31 While
globally homogeneous, composites are
locally heterogenous. These authors used
Monte Carlo simulations to generate
“samples” of small composites and studied
the size and number of systems needed to
reproduce, for example, elastic constants
of fiber-reinforced materials.
Figure 6. Structure factor Sq at wave vector q of fully protonated BPA-PC from simulation
(solid line) and neutron scattering (open squares).8 For comparison, results obtained with
a commercial ad hoc method for generating polymer structures (“Amorphous cell,” ꢀ) are
also shown.
roughly one repeat unit of the underlying
polymer. Thus, the objects under consid-
eration still contained many particles. On
this level, a number of other approaches
have been followed where mean-field
theories and random-walk statistics were
combined.23 The wide applications, espe-
cially for the understanding of morpholo-
gies of block-copolymer systems, can be
found in a series of papers by Fredrickson
and Bates.5 A commercially available simu-
lation program employing those and re-
lated methods can be obtained through
the MesoDyn project headed by Fraaije.24
We want to mention here another ap-
proach to coarse-graining the models fur-
ther.25–27 So far, the number of degrees of
freedom to be considered is proportional
to the number of monomers of a given
chain; in large systems with many chains,
this leads to a high number of degrees of
freedom to be monitored. To arrive at a
situation where one can simulate many
chains, we go back to Figure 1. The previ-
ous section discussed mapping between
the microscopic and the mesoscopic regime.
Now we consider the next step, namely, to
map the chains from the mesoscopic level
up to the semimacroscopic regime. The
chain is replaced by soft ellipsoidal par-
ticles, which will overlap in the melt. The
whole chain, or at least large parts of it, is
represented by one particle with three
internal degrees of freedom given by the
axes of the mass tensor R of the chain. To
do this, one can follow a philosophy very
similar to that of the coarse-graining pro-
cedures discussed before and separate the
free energy of a system into an intra- and
an interchain part.25 The intrachain contri-
bution to the free energy from chain i is
given by Fiintra ꢀ ꢁkBT ln P(Ri), where P(Ri)
is the probability of a mass tensor Ri of
chain i. This defines, as before, an intra-
chain potential of mean force. With the as-
sumption that the inter- and the intrachain
parts are additive, the interchain inter-
action is proportional to the pairwise den-
sity overlap ꢆi and ꢆj of the ellipsoids
representing the different chains i and j.
In a melt of chains of length N, approxi-
Conclusions and Outlook
Despite all of the progress made over
the last few years, a number of key chal-
lenges remain. On each level of descrip-
tion, new and improved methods have
been developed. Yet, significant progress
is still needed. Of most importance is the
controlled and systematic improvement of
links between the different simulation
schemes; for example, systematic coarse-
graining procedures, including the inverse
mapping step, need to be improved and
developed further. Steps must cover the
micro (many atoms) i meso (many
monomers) i macro (many chains)
regimes and link to quantum simulations
at the low end and to self-consistent field
calculations and/or finite-element-like
approaches at the upper end. This is cru-
cial in order to achieve the longstanding
goal of predicting material properties. The
efforts certainly are not intended to re-
place experiments; however, they should
in the long run help to reduce experimental
tests or allow much more focused testing.
One condition for this progress is im-
provement on each level of description,
such as
mately N chains overlap, thus the com-
ꢃ
putational cost per step can, at best, be
reduced by a factor of N. The most sig-
ꢃ
nificant time savings, however, comes
from the fact that, to a first-order approxi-
mation, the computational cost to run one
relaxation of the ellipsoids becomes inde-
pendent of N. This formula has been tested
on simple bead-spring polymer models.
An extension to a more refined coarse-
grained model (e.g., polycarbonate) is an
objective of current work. Within this
scheme, it was possible to simulate, on
ꢀ
Quantum simulations of reasonably
sized systems (Car–Parinello techniques,
path integral quantum Monte Carlo calcu-
MRS BULLETIN/MARCH 2001
209

Multiscale Problems in Polymer Science: Simulation Approaches
lations, and combinations of both), coupling
electronic and conformational degrees of
freedom.
Acknowledgments
5. F.S. Bates and G.H. Fredrickson, Phys. Today
52 (2) (1996) p. 32; G.H. Fredrickson and F.S.
Bates, Annu. Rev. Mater. Sci. 26 (1996) p. 501.
6. R. Martonak, W. Paul, and K. Binder, J. Chem.
Phys. 106 (1997) p. 8918.
7. W. Tschöp, K. Kremer, J. Batoulis, T. Bürger,
and O. Hahn, Acta Polym. 49 (1998) pp. 61 and 75.
8. J. Eilhard, A. Zirkel, W. Tschöp, O. Hahn,
K. Kremer, O. Schärpf, D. Richter, and U.
Buchenau, J. Chem. Phys. 110 (3) (1999) p. 1819.
9. G. Schöppe and D.W. Heermann, Phys. Rev. E
59 (1999) p. 636.
10. H. Meyer, O. Biermann, R. Faller, D. Reith,
and F. Müller-Plathe, J. Chem. Phys. 113 (2000)
p. 6264.
11. W. Paul and N. Pistoor, Macromolecules 27
(1994) p. 1249.
12. V. Tries, W. Paul, J. Baschnagel, and K.
Binder, J. Chem. Phys. 106 (1997) p. 738.
13. P. Doruker and W.L. Mattice, Macromolecules
30 (1997) p. 5520.
14. K.H. Haire, T.J. Carver, and A.H. Windle,
Comput. Theor. Polym. Sci. 11 (2000) p. 17.
15. R. Faller, F. Müller-Plathe, and A. Heuer,
Macromolecules 33 (2000) p. 6602.
16. H. Schmitz and F. Müller-Plathe, J. Chem.
Phys. 112 (2000) p. 1040.
17. K. Kremer and K. Binder, Comp. Phys. Rep. 7
(1988) p. 259.
The work described here is supported
by the BMBF Kompetenzzentrum Ma-
terialsimulation (Förd. Kennz. 03N6015)
and TMR grant No. ERB-4061-PL97-0661,
“New Routes to Understanding of Poly-
mer Materials” (NEWRUP). We would es-
pecially like to thank the many colleagues
and students who were involved in vari-
ous aspects of the described examples
over the years.
ꢀ
Improved methods to parameterize and
validate force fields for microscopic classi-
cal molecular simulations; suitably parame-
terized intermolecular interactions (for
polar molecules) are especially needed.
ꢀ
New methods for static and dynamic
studies on the semimacroscopic to macro-
scopic levels, such as dissipative particle
dynamics for composite materials.
These advances require a significant co-
ordinated effort of researchers coming
from different fields of expertise. Such proj-
ects are under way at a number of places
around the world and range from more
software-development-oriented activities,
such as the NEDO project in Nagoya, Japan,
and European efforts within the Training
and Mobility of Researchers program of
the European Commission, to more basic
method-development-oriented activities,
such as the “Center for Excellence in Ma-
terials Simulation” funded by the German
ministry of science and technology, which
is coordinated by our group.
References
1. K. Binder and G. Cicotti, Monte Carlo and
Molecular Dynamics of Condensed Matter Systems,
Vol. 1 (Oxford University Press, Oxford, 1996).
2. J. Baschnagel, K. Binder, P. Doruker, A.A.
Gusev, O. Hahn, K. Kremer, W.L. Mattice, F.
Müller-Plathe, M. Murat, W. Paul, S. Santos,
U.W. Suter, and V. Tries, in Advances in Polymer
Science: Viscoelasticity, Atomistic Models, Statistical
Chemistry, Vol. 152 (Springer-Verlag, 2000) p. 41.
3. K. Binder, ed., Monte Carlo and Molecular
Dynamics Simulations in Polymer Science (Oxford
University Press, Oxford, 1995).
4. L. Monnerie and U.W. Suter, eds., in Ad-
vances in Polymer Science, Vol. 116 (Springer,
Heidelberg, 1994).
18. D. Reith, H. Meyer, and F. Müller-Plathe,
Macromolecules (2001) in press.
19. W.H. Press, B.P. Flannery, S.A. Teukolsky,
and W.T. Vetterling, Numerical Recipes (Cam-
bridge University Press, Cambridge, 1986).
20. R. Faller, H. Schmitz, O. Biermann, and
F. Müller-Plathe, J. Comput. Chem. 20 (1999)
p. 1009.
21. F. Müller-Plathe, Comput. Phys. Commun. 78
(1993) p. 77.
22. O. Hahn, D.A. Mooney, F. Müller-Plathe,
and K. Kremer, J. Chem. Phys. 111 (1999) p. 6061.
23. F. Schmid, J. Phys.: Condens. Matter 10 (1998)
p. 8105.
24. P. Altevogt, O.A. Evers, J.G.E.M. Fraaije,
N.M. Maurits, and B.A.C. van Vlimmeren,
THEOCHEM J. Mol. Struct. 463 (1999) p. 139.
25. M. Murat and K. Kremer, J. Chem. Phys. 108
(1998) p. 4340.
26. F. Enrich and P. Maass, “Soft Ellipsoid Model
for Gaussian Polymer Chains,” preprint, Los
Alamos National Laboratories Preprint Server,
http://lib-www.lanl.gov/libinfo/preprints.htm,
cond- mat/0008425 (accessed February 2001).
27. P.G. Bolhuis, A.A. Louis, J.P. Hansen, and E.J.
Meijer, ”Accurate Effective Pair Potentials for
Polymer Solutions,” preprint, National Laborato-
ries Preprint Server, http://lib-www.lanl.gov/
libinfo/preprints.htm, cond-mat/0009093 (ac-
cesssed February 2001).
28. P.J. Hoogerbrugge and J.M.V.A. Koelman,
Europhys. Lett. 19 (1992) p. 155; J.M.V.A. Koelman
and P.J. Hoogerbrugge, Europhys. Lett. 21 (1993)
p. 369.
29. P. Español, Phys. Rev. E 57 (1998) p. 2930.
30. M.J. Turner, R.W. Clough, H.C. Martin, and
L.J. Topp, J. Aeron. Sci. 23 (1956) p. 805.
31. A.A. Gusev, J. Mech. Phys. Solids 45 (1997)
p. 1449; A.A. Gusev, P.J. Hine, and I.M. Ward,
Compos. Sci. Technol. 60 (2000) p. 535.
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